Your face is where the densest bones in your body are (especially your forehead), the back of your skull by comparison is very soft. This is why you’re more likely to break your hand punching someone in the face than you are other places on their body. Your ex-army colleague is correct, hitting the back of your head is much more dangerous than the front.

It’s… killing someone with one punch is either damn lucky, or damn unlucky depending on how you look at it. It’s a fluke. You need the stars to align for it to happen. A human being is highly unlikely to naturally land on the back of their head, especially when no attempt is made to direct their fall. Even if a punch knocks them off their feet, the way the body falls works against it. (They can hit things on the way down, but that’s a different issue. You also don’t want to be punching them in the face.) If you want to direct a fall, then I’m going to point out that this is why throws like the kind specialized in judo, jiu-jutsu, and aikido exist. They’re all about controlling how someone hits the ground, how hard, and where, usually in an unpleasant way.

Your body does have natural instincts (not relevant to combat instincts) to protect the vital pieces of itself, your head is one of those. It doesn’t have the sense to get out of the way of a punch, but you’re far more likely to land on your butt or your back than directly on your head. Even if you do manage to hit your head, in a natural fall, some other part of your body will hit the ground first and negate a portion the force. (This is why, in many martial arts, students are trained to fall before they learn anything else. When you see people slapping the ground, that’s what they’re doing. They’re countering the force of the fall, absorbing it with the roll, and dissipating some of it with the slap rather than taking the full force of the blow on their back, shoulder, or wherever else that is likely to be more damaging.)

So, say you get punched in the face, and the force of the blow is enough to knock you off your feet. If you rock back on your heels and fall, what does your body start to do? Your knees bend, and you land on your ass.

You can force someone to fall on their head, or their face, but it isn’t with a punch. This is (partially) what sweeps are for. A sweep is when you use your ankle or your leg to pull your opponent’s feet out from underneath them. Say you want to force a fall as a technique that isn’t one of the more common throws. If you’re close enough, you step past them and place your leg behind theirs. Your hand goes to their head, or their chest, and you shove. Usually, with this particular technique, you ride them all the way down to ensure maximum effect and drive their chest/head into the ground.

Taking someone by their head and ramming it into a wall will be more dangerous to them than using their forehead, and so on.
With falls, it depends on your control, what you know how to do, and what your options are. There are an abundance of options when it comes to controlling your opponent on the way down if you know how to carry it off and are lucky enough to pull the technique off. Wrench, pull, push, drag, etc. Some martial arts with a peaceful focus like Aikido aim for their throws, at the highest levels, to cause no damage at all.

The truth is you are far more likely to break your wrist in a bad fall than you are your head.